First use of triply labelled water analysis for energy expenditure measurements in mice

The doubly labelled water (DLW) method is widely used to determine energy expenditure. In this work, we demonstrate the addition of the third stable isotope, 17O, to turn it into triply labelled water (TLW), using the three isotopes measurement of optical spectrometry. We performed TLW (2H, 18O and17O) measurements for the analysis of the CO2 production (rCO2) of mice on different diets for the first time. Triply highly enriched water was injected into mice, and the isotope enrichments of the distilled blood samples of one initial and two finals were measured by an off-axis integrated cavity output spectroscopy instrument. We evaluated the impact of different calculation protocols and the values of evaporative water loss fraction. We found that the dilution space and turnover rates of 17O and 18O were equal for the same mice group, and that values of rCO2 calculated based on 18O–2H, or on 17O–2H agreed very well. This increases the reliability and redundancy of the measurements and it lowers the uncertainty in the calculated rCO2 to 3% when taking the average of two DLW methods. However, the TLW method overestimated the rCO2 compared to the indirect calorimetry measurements that we also performed, much more for the mice on a high-fat diet than for low-fat. We hypothesize an extra loss or exchange mechanism with a high fractionation for 2H to explain this difference.


Material and methods
Animals and housing. Twenty male C57BL6/J mice were individually housed on a 12:12 light-dark cycle with food and water ad libitum, and a controlled temperature (22 ± 1 °C) (more details in Ref. 13 ). At the age of 27 weeks, ten of the mice were maintained on regular chow diet, the so-called low-fat diet (LF) group (17.5 kJ/g; fat content 13.5%; protein content 28%; carbohydrate content 58%). The other ten mice were changed to a highfat sucrose diet (HF) (21.8 kJ/g; fat content 28%; protein content 19.5%; carbohydrate content 52.5%) eleven weeks prior to the TLW injection.
Preparation of the triply labelled water. We produced a highly enriched TLW mixture by mixing the 2 H, 18 O and 17 O "mother" waters (around 8.0, 12.4 and 6.2 g, respectively, determined with 0.1 mg precision). The "mother" waters are purely 2 H water ([ 2 H] > 99.9%, Sigma-Aldrich, Netherlands), 18  ). This is equivalent to enrichment factors of ≈ 1900, 280 and 225, respectively, so in our experiments we expect higher enrichments for δ 2 H than for δ 18 O and δ 17 O, whereas the latter two will be roughly equal. Given the measurement uncertainty of our Off-Axis Integrated Cavity Output Spectroscopy (OA-ICOS) analyzer, we expect similar accuracies in the measurements for all three isotopes this way.
Using this mixture for the injection in the mice, we estimated that a 0.17 g injection would result in the initial samples (the most enriched ones) having δ 2 H and δ 18 O values close to the international enriched reference water IAEA-609 (δ 2 H = 16,036.4‰, δ 18 O = 1963.7‰ 35 ). Therefore, the suite of enriched water references IAEA-609,608 and 607 are suitable for δ 2 H and δ 18 O calibration of all mice blood samples. However, as these reference waters are not (or only mildly) enriched in 17 O, we cannot use them for the calibration of our δ 17 O measurements, where we expect initial values of around 1700‰. Therefore, to calibrate TLW measurements, we made a range of four reference waters enriched in all three isotopes, by gravimetrically mixing the highly enriched TLW mixture ( . Different amounts of the TLW mixture, from 0.25 to 0.6 g (~ 0.1 mg precision), were put into a 2 ml glass vial, and then immersed into a glass bottle which contains about 100 g demineralized water (~ 0.1 mg precision). These bottles were sealed after mixing and shaken periodically for several hours. Table 1 shows the values of these four TLW-references along with their uncertainty. The δ 2 H and δ 18 O values were measured by OA-ICOS and calibrated using IAEA-609, 608 and 607. The error of δ 2 H is based on several measurement repetitions, but for δ 18 O, the measurement uncertainty is small (less than 1‰), so the uncertainty of IAEA waters are important for the δ 18 O error of these TLW-references 35 .
The IAEA waters are unfortunately only mildly enriched in 17 O, so for the δ 17 O value determination of our four TLW reference waters, we conducted several dilution experiments to bring the resulting δ 17 O values of the diluted TLW reference waters within the range of the IAEA waters (with IAEA-609 having the maximum δ 17 O value of 126.6‰). By using the accurately determined dilution factor, we could in this way calibrate the δ 17 O of TLW reference waters using IAEA-609,608 and 607. All calculations of isotope abundances and δ-values were performed using a thoroughly validated Excel spreadsheet 36 . Based on the measurement uncertainties, the uncertainties in the values quoted for the IAEA waters, and the dilution uncertainties we attribute a conservative ± 1% relative uncertainty to our δ 17 O values (see Table 1). Besides the best estimates for the δ 17  Experimental design. For the experiments, each mouse was intraperitoneally injected with about 0.17 g (weighted to the nearest 0.1 mg) of the highly enriched TLW mixture. Before injection, we took 4 blood samples separately from 5 mice for background isotope analysis. After exactly 2 h after the TLW injection, the initial blood samples were taken. Then, the mice were transferred to the indirect calorimetry (IC) cages for two consecutive days. The indirect calorimetry (IC) was shortly interrupted at exactly (deviations less than 2 min) 24 and 48 h after the initial sample time. In this study, the background and TLW mixture blood were all sampled by tail snip (4 times per sample every time), and then flame-sealed into 25 µl glass capillaries until the micro-distillation process 13 . Mice body masses were measured by a balance (~ 0.1 g precision), and fat, lean weight and water content of all the mice were measured by a magnetic resonance imaging machine (EchoMRI-100, Echo Medical Systems, Houston, TX, US) just before injection 37 . All experimental procedures were approved and guided by the local Animal Experimentation Committee (DEC) of the University of Groningen.
Indirect calorimetry. In the IC cages (Homemade polypropylene cage, 43 × 30 × 21 cm), the housing and feeding conditions were not changed. The detailed description of the IC method in our lab is in Ref. 13 . The IC system measured the O 2 and CO 2 concentration difference of the dried inlet air (3 Å molecular sieve drying beads; Merck, Darmstadt, Germany) and dried outlet air going through the chambers. The flow rate of the inlet was set at 20 l/h, and only 6 l/h outlet air passed through the drying system and subsequently to the gas analyzers. The mass-flow controllers (Type 5850; Brooks Instrument, Veenendaal, The Netherlands) were calibrated before and after the trials (the variation < 1%). O 2 was measured by a paramagnetic O 2 analyzer (Xentra 4100, Servomex, Egham, UK), and CO 2 by an infrared gas analyzer (Servomex 1440). The CO 2 and O 2 analyzers were calibrated daily with two certified gas standards (Linde Gas, The Netherlands), with values 19.5612% for O 2 and 0.0006% for CO 2 , and 20.8743% for O 2 and 0.5133% for CO 2 , respectively. The maximum overall error of the method is ≤ 2%. For validation purposes, the respiratory quotients (RQ = r CO2 /r O2 ) and metabolic rates (MR) were also recorded and calculated 13,38 . Analysis method of the TLW samples. The δ 2 H, δ 17 O and δ 18 O of mice blood samples and reference waters were measured by a commercial Off-Axis Integrated Cavity Output Spectroscopy (OA-ICOS) Liquid Water Isotope Analyser (LWIA 912-0050, Los Gatos Research, San Jose, CA, USA). Before injection into the analyser, all the samples and references were prepared by a home-built micro-distillation system (detailed distillation procedures are described in Ref. 39 ). In brief, a capillary is broken in an evacuated system, and the water is collected in a freeze finger immersed in liquid nitrogen. The system is then again evacuated, and the water is finally transferred, again using liquid nitrogen, into a small insert tube, which can be measured directly on the OA-ICOS analyser. The reference waters (the IAEA series and our TLW references) are treated identically, so also transferred from capillaries.
The distilled samples and references were introduced into the OA-ICOS instrument through an auto-injector (Pal, CTC Analytics, Zwingen, Switzerland), and there is a heated injector block to evaporate the liquid water. This vapour expands into a high-finesse optical cavity, and the δ 2 H, δ 18 O and δ 17 O values were calculated from fits to the relative transmission spectrum. The distilled IAEA-609,608 and 607 and our local TLW references are interleaved with samples during the measurement series for calibration and instrumental drift correction. Each reference and sample water was injected 12 times. Before each distillate reference, the same reference water, but without distillation, is also injected 12 times to check the micro-distillation quality and stability, and also to reduce memory effects. However, only the distilled references were used for calibration. www.nature.com/scientificreports/ Raw data from the instrument were analysed using a bespoke data analysis program (written in R), through which memory effects and drifts were corrected, and calibration was performed (for details see 40 ). Specifically, to correct for memory effects we do not ignore the first few injections of a sample, but instead use all of them and correct for the memory effects using a 2-3 pool exchange algorithm 39 . This is quite meaningful for TLW blood samples, which have a minimal sample size (less than 15 µl). Figure 1 shows a representative part of a measurement batch (containing "initial" samples), in which both the raw, and memory corrected values for several samples and reference waters are shown. The improvement in precision is remarkable: standard deviations of the 12 δ 2 H measurements of the samples around 6000‰, for example, reduce from 210 to 30‰ when measured just after natural (demineralized Groningen tap-) water (δ 2 H ≈ − 42‰).
For calibration, mostly a "multiple-point" quadratic fit is chosen, which is based on three or more of the reference waters. This is based on our experience that for these highly enriched samples and the large range in δ-values in each series (e.g.: δ 18 O from 736 to 1963‰ for the IAEA reference waters), the instrument's output is not fully linear. This is probably due to imperfect line fitting, which also makes itself noticeable through relatively high values for the so-called "Narrow Band" spectroscopic interference 41 . This tool is meant to be an indicator for contamination, but as contamination does not occur in our samples (and certainly not in the pure reference waters), here it is the result of an imperfection in the spectroscopic fit of these triply labelled waters.
As illustrated in Ref. 39 , duplicate analysis of DLW samples is necessary and helpful, due to the dominant uncertainty contribution of the actual procedure of flame-sealing and micro-distillation. In this study, if the δ 2 H value of a duplicate analysis deviates more than 2% of its value from the first (or 1.5% for δ 18 O, 1.5% for δ 17 O), a third sample is analyzed. A third sample is also taken if the quality of a capillary is questionable (for example not tight or containing too much air). The average of the duplicate (or triplicate if an outlier cannot be identified) analyses, along with the standard error in the mean is taken as the final result. The OA-ICOS measurement uncertainty for individual samples is usually negligibly small compared to the spread between duplicate samples.
For the TLW method analysis, we use isotope abundances instead of the δ-values. First, the sample's x δ s values need to be converted into abundance ratios x R s (x = 2, 17 and 18), using the isotope abundance ratios for Vienna Standard Mean Ocean Water (VSMOW), which are 1.5576 × 10 -4 , 3.799 × 10 -4 , and 2.0052 × 10 -3 for 2 H, 17 O and 18 O, respectively 42 : From these ratios, the absolute isotope concentrations x C s are computed, usually expressed in parts per million (ppm): www.nature.com/scientificreports/ Calculations. After the injection of the enriched TLW mixtures into the mice, the enriched rare isotopes are gradually exchanged with the surroundings, and the turnover rate (k; h −1 ) describing the rare isotope concentration decrease can be expressed as: C is the concentration of the isotope 2 H, 18 O or 17 O. "i" means the initial, and in this study, the initial sample is the 2-h samples taken after injection. "b" is background (concentrations corresponding to δ 2 H = − 27.3‰, δ 18 O = − 4.85‰, δ 17 O = − 2.61‰, as established based on sampling five mice prior to the injection of TLW), and "f " is the the final sample (taken either 24 h or 48 h after the initial sample), therefore, time duration "t" is equal to 24 or 48 h.
The dilution space of the isotopes in the body, and thus the size of the body water pool, can be calculated using the measurement of the initial concentration by the so-called plateau method 4 : where N (mol) represents the dilution space or body water pool for 2 H (N 2H ), 18  In this expression, the loss of enriched isotopes in the 2 h between the injection and the initial measurement is ignored. Alternatively, one can take this loss into account by extrapolating the turnover rate back to the injection time. This is called the intercept method 4 : where C i-ic is the concentration extrapolated back to the time of injection (0 h), and t i -t inj is equal to 2 h in our case.
Whereas the plateau method is expected to underestimate the body water pool slightly (as the loss of enriched isotopes during the first 2 h is ignored), the intercept method, on the other hand, possibly overestimates the body water pool, as the loss of enriched isotopes during the first two hours is probably less than later, since the enriched isotopes have not distributed themselves over the entire body water pool. Therefore, calculating and comparing both is a good practice.
It is generally observed that the body water pool as determined by 2 H is slightly, but significantly, larger than that by 18 O 4,13,43 . This is commonly attributed to the exchange of hydrogen (and thus 2 H) with body tissues, which does not occur with oxygen. For this reason, we expect the body water pool determination using 17 O to be identical to that with 18 O.
The amount of total body water (TBW, g) for each individual animal is then simply: M is the molar mass of water (18.02 g/mol). In terms of carbon dioxide production, in a simple expression ignoring the fractionation effects, the difference between 2 H and 18 O turnover is proportional to the rate of CO 2 production (rCO 2 ; mol/h): Also here, several fractionation effects occur in the process. Therefore, this Eq. (10) is not suitable for an accurate calculation of rCO 2 . However, as the deviations are relatively small, this equation can be used for uncertainty propagation calculations. The full expression contains the following fractionation factors: the (partly kinetic, partly equilibrium) evaporation of water for 2 H (f 1 ) and 18 O (f 2,18O ), and the CO 2 -H 2 O fractionation for 18 O (f 3,18O ), which is assumed to be in equilibrium: r G is the fraction of the water loss due to evaporation, as it happens in the lungs. By lack of a firm determination or estimate, most studies use a value of 0.5. The isotopic fractionation process leads to relatively lower abundances of the heavy isotopes in the vapour phase. All fractionation factors are shown in Table 2 where k 17 is the turnover rate for 17 O, and f 2,17O and f 3,17O are the fractionation factors for 17 O fractionation in the water evaporation and the CO 2 -H 2 O equilibrium, respectively.
In Table 2, we list the fractionation factors obtained from literature, as well as the 'mixed' results by the equilibrium/kinetic as a ratio of 3:1 4 , and the final (f 2 -f 1 )/2f 3 calculation results. All the factors are equal to the There are several classical equations to calculate the CO 2 production, which differ in the selection of fractionation factor values, portion of fractionation water (r G ) and body water pool models, and are also dependent on the research subjects (animals or humans) 4,16,[45][46][47] . Equations (11) and (12) use a single pool model, they are reproduced as equationns 1-1 and 1-2 in Table 3. For 18 O, equation 1-1, is similar to the expression in Ref. 4 except the number of decimal places, and equation 1-2 is for 17 O based on the same calculation principle. When we consider the two-pools model, which means that the effective body water pool is taken differently for 2 H than for 18 O (or 17 O), the Coward 1985 46 and Speakman 1993 45 models are more logical and suitable for animal CO 2 production calculation. The equations 2-1, 2-2, 3-1 and 3-2 in Table 3 are based on their model principle, separately from Coward 1985 46 and Speakman 1993 45 . The fractionation factors (from Table 2) used for the equations in Table 3 are the same, irrespective of the model. The R dil in 3-1 and 3-2 is the mean dilution space ratio N 2H /N O (the dilution space calculated by 2 H divided by the dilution space calculated by 17 O or 18 O) for different group members, so different for the low and high fat diet mice.
Ethics approval. All experimental procedures involving animals were approved and guided by the local Animal Experimentation Committee (DEC) of the University of Groningen.

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Results
Body composition. After 11 weeks on a high-fat diet, the high-fat diet mice gained more than 5 g of weight.
On the basis of the body mass gain (> 10 g or < 10 g), 5 mice were assigned to be obesity-resistant (HF-OR), and 5 mice were in the obesity-prone (HF-OP) group. The body mass weighed just before injection were used as body weight, together with the fat mass, lean mass, and body water measurement by EchoMRI. From the 10 mice on low fat diet (LF), two had to be discarded from the data set due to blood sampling problems (only one successful capillary for the initial sampling, and large discrepancies between their calculated total body water by TLW and by EchoMRI). Figure 2 illustrates the average values of the body-weight, lean content (g), fat percentage (fat/body-weight) and body water percentage (body-water/body-weight) of the three mice groups: LF, HF-OR and HF-OP (with 8, 5 and 5 individuals, respectively). When analyzing the individual differences in body content, we find that the fat percentage is positively correlated with the body-weight, and negatively correlated with the body-water percentage. When analyzing the group difference, Fig. 2 clearly shows that the HF-OP mice group, which is heaviest (the average 45 g), has the lowest water percentage (the average 50%) and the highest fat percentage (37%). The  www.nature.com/scientificreports/ average weight difference between the LF and HF-OR groups is not large (30.6 g and 33.8 g, respectively), but the fat-% and water-% are quite different. The lean contents for LF and HF-OR groups are similar (nearly 24 g), and the average lean content of the HF-OP group is only 2.5 g higher than the other two groups.
Indirect calorimetry. After taking the initial blood samples, the 20 mice were put into the indirect calorimetry box and the actual r CO2 , r O2 and RQ were measured over the two following days. The data around the interruptions (taking blood samples) were removed, and the IC data summary of the two days is listed in Table 4. Table 4 also shows the mean food intake (kJ/day) for the three categories. The individual variability is large (especially for the HF-fed mice), but on average the LF mice have taken in a higher caloric value of food than the HF ones.
All observed values are equal within the error for day 1 and day 2, except for r CO2 of the LF mice. The r CO2 of the LF and HF-OR groups are similar and their difference is within the error, but the CO 2 production of the HF-OP group is about 8 ml/h more than that of the other two groups. The r O2 values differ significantly between the groups, and that of the HF-OP group is the highest.
The respiratory quotient (RQ) resembles the low-fat or high-fat food intake difference between the LF and the two HF groups. There is no difference between the HF-OR and HF-OP groups, and they are both lower than the RQ values of LF. As the Metabolic Rate values are directly computed from r CO2 and the RQ, they show the same trends. The MR value of HF-OP is highest (about 5 kJ/day more than HF-OR, 11 kJ/day more than LF).
Turnover rates k. The turnover rates for 2 H (k 2H ), 18 O (k 18O ) and 17 O (k 17O ) were separately calculated from the logarithmic decline of the initial isotope abundance (2-h after injection) and the isotope abundance of two finals (24 h and 48 h after the initial sample taken). The average k 2H , k 18O , k 17O for the three mice groups are  Table 4. Indirect calorimetry (IC) measurement results for 2 days, expressed as mean ± standard error (SE). Day 1 means the first 24 h in the IC box after the initial samples taken, and Day 2 is the second 24 h. rCO 2 and rO 2 are the CO 2 production and O 2 consumption in ml per hour, RQ is the respiratory quotient. The metabolic rates (MR) are calculated based on Ref. 38 . The lowest rows give the mean food intake (kJ) ± SE for the three categories.  Fig. 3, whereas Table 5 gives the numerical values, and in addition the turnover rate ratios and differences. All are presented for the 24 h and the 48 h period. It is clear that the LF group has the highest turnover rates of the three groups, and the differences are highly significant between LF and HF groups. The turnover rates of the HF-OR group are slightly higher than the HF-OP group, but for k 2H and k 18O , the difference is not significant. In Table 5, it is clear that the uncertainty in k-48 h is lower than that in k-24 h, this is because of the larger difference between the isotope values for the 48 h-finals and the initials. In Table 5 and Fig. 3, for k 2H , we can see the difference between 24-and 48 h is significant, k 2 -48 h being higher than k 2H -24 h for all three mice groups. For k 18O and k 17O , on the other hand, the differences between the turnover rates for 24 h and 48 h are small and not significant. The k 17O and k 18O agree with each other within the uncertainties for both of the two times. This is to be expected, as both the 17 O and 18 O label are subject to the same processes. The fact that they do agree within the uncertainty increases the confidence in the experimental results (both the animal handling side and the isotopic analysis of the blood samples). Therefore, it is possible to obtain the turnover of oxygen by taking the average of k 17O and k 18O , which lowers the uncertainty of k O (turnover for oxygen isotopes).

Time LF (n = 8) HF-OR (n = 5) HF-OP (n = 5)
As shown in Table 5, the turnover rates ratios k O /k 2H are typically 1.9 (LF) and 2.3 (HF) for 24 h finals, while for 48 h, they are a bit lower: 1.7 (LF), 2.0 (HF), fully caused by the increase of k 2H . In the analysis of k O -k 2H , which carries the r CO2 signal information, the k O -k 2H values are obviously lower for 48 h than for 24 h because of the higher k 2H -48 h values. On the other hand, the differences between the three groups for the same final are not significant in most of the cases, expect the k 17O -k 2H for HF-OR group at 48 h-final.
Total body water (TBW) and dilution space. The body dilution space (N) can be measured based on the plateau method (Eq. (6)) or on the intercept method (Eq. (7)), and the total body water is calculated using Eq. (9). In Fig. 4 we compare the body water percentage (water/mass) results calculated by TLW with those by EchoMRI. To illustrate the differences better, Fig. 4 shows the differences between the two. In terms of individual variation, the water percentage values from the calculation (TLW) and measurement (EchoMRI) are consistent with each other (not shown here). Moreover, the dilution space difference obtained by the intercept method   17 O (k 17O ); turnover rates ratio: k 18O /k 2H and k 17O /k 2H ; turnover rates differences (10 −3 h −1 ): k 18O -k 2H and k 17O -k 2H . The ratios and differences are calculated from the individual initial isotope abundances (2-h after injection) and two finals (24 h and 48 h after the initial sample taken), and are expressed as mean ± SE.  Fig. 4. It is clear in Fig. 4, and expected (see above), that the plateau method gives higher water percentages than the intercept method for both 2 H, 18 O, and 17 O, and also that the water percentages based on 2 H are the highest (nearly 2% higher than the EchoMRI values for the plateau method). On the other hand, the intercept method results for 18 O and 17 O give lower water percentages than that of EchoMRI. Still, given the combination of the indicated uncertainties for the TLW method (as indicated in Fig. 4) and the uncertainty of the EchoMRI method (estimated to be ≤ ± 2%), all differences shown in Fig. 4 are not significant. Furthermore, although the water percentage values for the three different mice groups are different (see Fig. 2), the differences between the TLW and EchoMRI methods do not seem to correlate with these percentages themselves.

Mice group k 2H (10 -3 h −1 ) k 18O (10 -3 h −1 ) k 17O (10 -3 h −1 ) k 18O /k
The absolute total body water or dilution space (N) values calculated by three isotopes and two methods are listed in Table 6 for the three mice groups. As Fig. 4 already showed, the values of the plateau method are higher than that of the intercept method for each mice group irrespective of the isotope used. N 2H is always higher than N O , and N 17O matches N 18O . The most important feature in Table 6 is that the dilution space of HF-OP group is significantly higher than that of LF and HF-OR, while the dilution spaces of HF-OR and LF are equal for most of the cases. CO 2 production. The average r CO2 of each LF, HF-OR and HF-OP group are calculated by three kinds of equations which are listed in Table 3. We took the r G = 0.5. The r CO2 results are shown in Fig. 5, and for each group, there are two kinds of doubly labelled water methods: left columns based on 18 O and 2 H, and right columns based on 17 O and 2 H. We also consider the different dilution space (N) calculation methods (plateau or intercept methods) and two different finals (24 h or 48 h). The grey horizontal line in the bottom is the average r CO2 value for 2 days from the indirect calorimetry method for the three mice groups. Therefore, in summary, we consider 4 factors for each mice group to calculate the r CO2 : two finals (24 h or 48 h), two N calculation methods (plateau or intercept), three models (Table 3 4 For all three mice groups, the 24 h r CO2 data are much higher than the 48 h data, irrespective of the calculation method, in other words, the differences between solid and hollow symbols in each column are the same. The differences are all caused by the k 2H -48 h value being larger than the k 2H -24 h one (see Fig. 3, Table 5). Of course, this difference could indicate a real different behavior, but the IC values for the two days do not show . Body water percentage differences between TLW (both 2 H, 18 O, and 17 O) and EchoMRI for the three mice groups, expressed as mean ± SE. Plat-means using the plateau method (Eq. (6)), an int-means using the intercept method (Eq. (7)). The uncertainty for the EchoMRI values is estimated to be 2%. www.nature.com/scientificreports/ such a difference (Table 4). In terms of different oxygen isotopes for each mice group, the difference is random (from 0 to 8 ml/h), just within the largest errors no matter which model is used. For each of the oxygen isotope and models in each mice group, the r CO2 calculated by the intercept method (yellow area) is lower than that by the plateau method. However, the differences are within the uncertainties. Interestingly, the intercept points are more scattered than the plateau ones, caused by the extra influence the turnover rates k have when using the intercept method. As was stated before, one can expect the plateau method to give an overestimation of the water pool size, and the intercept an underestimation. This results in and over-and underestimation of the r CO2 , respectively. The average of the two values would probably produce the best result, while their differences would give an estimate of the uncertainty. Obviously, the most striking feature of Fig. 5 is the discrepancy between all the TLW results on the one hand, and the IC results on the other. The discrepancy is the smallest for the 48 h two-pools models, with the solid triangles (Coward 1985, 48 h-) having the lowest discrepancy with IC for each mice group. The lowest difference of TLW and IC is 8 ml/h (LF) and 16 and 15 ml/h (HF-OR and HF-OP) for these results (the equation 2-2 for 48 h). The TLW and IC results agree in the sense that both show the highest r CO2 for the HF-OP group. However, the average IC values for the HF-OR and LF groups are similar, while in the TLW methods, the r CO2 of HF-OR is higher than the r CO2 of the LF group (about 10 ml/h).
The discrepancy between TLW and IC needs an explanation. Figure 6a shows the individual r CO2 measured by the 2-1 and 2-2 (Coward 1985) models with the intercept method at 48 h finals, and the individual IC values of day two. It is very clear that r CO2 measured based on the 18 O-2 H and 17 O-2 H pairs are consistent, and their difference is within the uncertainty. For the LF and HF-OP groups, the r CO2 ( 18 O) is slightly higher than r′ CO2 ( 17 O), but the difference is only about 4 ml/h and not significant. Figure 6b clearly illustrates the deviation of the TLW and IC methods. The r CO2 values of the TLW method are calculated by averaging the r CO2 ( 18 O) and r′ CO2 ( 17 O), and the IC r CO2 values are the same as in Fig. 6a. The uncertainty in the difference (TLW minus IC) in Fig. 6b is around 3.5 ml/h (based on 3% relative error for TLW and 2% for IC). The average difference between the TLW and IC values for the LF mice is 7.2 ml/h, while the average distance between TLW and IC for HF groups is 18.1 ml/h, much larger than that of the LF group. The individual IC and TLW data show a similar pattern, which is a firm indication that the difference between TLW and IC is of a systematic nature. As the IC technique is straight forward and less assumption-prone, we suspect the deviation to be caused by isotopic effects not accounted for.

Discussion
The triply labelled water method. Because the measurement of δ 17 O has become simple, fast and accurate by the optical spectroscopic system, the classical Doubly Labelled Water (DLW) can easily be extended to Triply Labelled Water (TLW), and to our knowledge we demonstrated that here for the first time. The isotope abundance measurement uncertainties of 17 O and 18 O in the blood samples are similar, and the individual turnover rates of 17 O and 18 O are also expected to be equal no matter the subject treatment or the turnover time chosen, and our data confirmed this (Fig. 3). The same holds for the dilution space difference between N 17O and www.nature.com/scientificreports/ N 18O (Fig. 4). In terms of r CO2 calculated based on 18 O, 2 H, or on 17 O, 2 H, the values also match with each other for the same models (Fig. 5). These findings are consistent with our assumptions: although processes with 17  Another use of the third isotope is to help quantify the evaporative water loss fraction, in other words, the TLW method enables us, at least in principle, to derive a direct estimate of the fractionated losses fraction (r G ). This value of fractional evaporative water losses-r G -has been subject of discussion since many decades 4,5,48,49 . As the r CO2 ( 18 O, 2 H) should be equal to r′ CO2 ( 17 O, 2 H), we can derive the individual r G values by equating the two Eqs. (11) and (12). However, the influence of the value of r G is limited: in this paper, we took r G = 0.5, a value that is also widely used in free-living mammals. If we would use r G = 0.25 as other researchers have done 4,48 , the r CO2 will increase by less than 2%, which is within the uncertainty band of our TLW average values (3%). Alternatively, one can say that in order to determine r G from the combination ( 18 O, 2 H) and ( 17 O, 2 H) to ± 0.1, one would need an uncertainty in r CO2 ≤ ± 1%, out of reach of the present measurement methods, as was already concluded in Ref. 5 .
At the moment, highly enriched 17 O water is more expensive than pure 18 O water, this is mainly because of less demand for it. However, 17 O can now be easily detected by the optical systems such as the one we use. Also, one only needs a factor of 7 less 17 O label to achieve the same enrichment factor as for 18 O water, and this reduces the costs. Therefore, adding 17 O to the classical DLW method is practically easy now, and it is also worthy to use TLW to check the method and improve the precision of the CO 2 production. At the moment, certified reference waters (such as Ref. 35 ) are not yet available for highly enriched 17 O, so laboratories should make their own references by gravimetrical mixing. However, if demand increases, such reference waters will be made available, by international bodies such as IAEA, or commercial suppliers.
Calculation protocols. We considered three models for CO 2 production, one is based on the single-pool model (1-1 and 1-2 in Table 3), another two series of equations are based on the two-pools model (Table 3). In addition, we used the best available values from the literature for the fractionation factors (including 17 O). The two-pool equations based on Ref. 46 take the individuals' specificity more into account, while the equations based on Ref. 45 use a group average for the dilution space ratio. Therefore, we consider the equations based on Ref. 46 to be the best form a principal standpoint. Nonetheless, we compared two different group averaging methods for R dil in equations 3-1 and 3-2, one is for the whole group of 18 mice regardless of the feeding methods, the other is separate averages for the three mice subgroups (as used for Fig. 5). Differences in r CO2 were less than 2%, so the group difference of R dil is not essential. The results in Figs. 5 and 6 show that the r CO2 calculated by Ref. 46 are indeed closer to the CO 2 production obtained by indirect calorimetry, but there still is a significant discrepancy, much larger for the 24 h results than for the 48 h ones, and much larger for HF groups than LF groups: The TLW method leads to higher numbers for the r CO2 .
We found a clear increase from k 2H -24 h to k 2H -48 h, but no significant change for k 18O and k 17O . This leads to increased values for r CO2 in the first 24 h compared to the second 24 h. One might speculate that this can be caused by the disturbance of the mice during the first day: we injected the labelled water, took the 2 h as well as www.nature.com/scientificreports/ the 24 h blood samples and put them in and out of the IC box at the first day, but we only took the 48 h samples on the second day. However, the IC results show no significant changes between the first and second day. Due to this low k 2H -24 h, the TLW r CO2 results for the 24 h deviate much more form the IC results than the 48 h results (see Fig. 5). Still, also the 48 h results for rCO2 are high compared to the IC result, which fact one could alternatively formulate as: k 2H -24 h is much too low, k 2H -48 is still too low, but by less. If we consider the IC results as straight forward and trustworthy, this would lead to the speculation that the 2 H label disappears form the body water at a lower rate than the water loss itself, so involving a process with very high fractionation. We discuss this possibility further below, in which discussion the extension of DLW to TLW appears useful.
Influence of the nutritional conditions. Previous work in our lab focused on different nutrition and body composition effects on r CO2 of mice by the DLW technique 13 . They also separated their mice in the same three groups, only their mice were younger. They also found that the r CO2 measured by DLW matches IC results much better for low-fat mice than for the high-fat feeding mice, so the high-fat diet is a relevant factor to explain the overestimation of DLW. Intuitively, one might expect that the high-fat fielding mice would consume a higher caloric value of food than the low-fat ones, but this appears to not be the case, rather the opposite (Table 4). However, the individual scatter is large, and does not correlate at all with the individual deviation between IC and TLW values for r CO2 . Rather, the main difference we consider between our three groups is the turnover rates difference (k O -k 2H ), because the TLW-determined body water agrees well with the EchoMRI-determined one, implying that the dilution space for the water is correctly determined. Yet, the r CO2 determined by TLW is systematically higher than that with IC, even for the "most agreeing" calculation method (see Figs. 5,6). This difference is the lowest, regardless of the individual difference, for the LF mice group, close to 8 ml/h, still significantly higher than the largest error of TLW (± 3%) and IC (± 2%). For the HF-OR and HF-OP mice groups, this difference is more than double that amount. The (too) high r CO2 values must be caused by too low k 2H -values, and/ or too high k 17O and k 18O ones. The number of possible explanations is limited, because the body water pool is correctly determined by TLW. The only thinkable way of getting too high 18 O and 17 O rates is assuming a strongly fractionating water loss process that preferably takes up 17 O and 18 O over 16 O, and with the same fractionation factor for both. Such a process is next to impossible to imagine, as fractionation factors for 17  H on the other hand, we would need an extra water loss or uptake process that heavily discriminates against 2 H, and such processes are thinkable, and in fact known: electrolysis of water, for example, manifests fractionations of − 600 to − 700‰ (so fractionation factors of 0.4 to 0.3), and also bacterial uptake is known to fractionate considerably (albeit not to the extent of electrolysis). A rough calculation shows that if a 10% extra loss/exchange effect would exist with a 2 H fractionation factor of 0.4, this would lead to an overestimation of r CO2 by 10 ml/h. As the effect is considerably larger for the 24 h than for the 48 h results, the process might in fact be an exchange effect that reaches equilibrium at some point. If that is the case, the TLW-IC difference must gradually disappear. As the discrepancies are much larger for the HF than for the LF mice, body composition (fat content) and/or food digestion must play a profound role in this mechanism. Identifying the cause of the discrepancy with IC is essential for the reliability of the DLW/TLW methods alike. Thanks to the addition of 17 O, the mechanism must be some kind of fractionating 2 H loss. This requires further study, and eventually inclusion of that mechanism into the equations of Table 3.

Conclusions
This study extends the traditional doubly labelled water technique to triply labelled water to estimate the CO 2 production for mice held in different nutrition conditions.
The results for both combinations 2 H-17 O and 2 H-18 O agree well, and hence the calculated r CO2 uncertainty is lower and the values are more robust. However, we found that systematic deviations between the DLW (now TLW) method and indirect calorimetry still exist 13 . Thanks to the addition of 17 O, we can now conclude that a process of extra water removal/uptake with a high degree of discrimination against 2 H must be the cause of the too high r CO2 results. This uptake apparently is dependent on the food intake and/or the body composition. More detailed isotope analysis (such as gastric fluids 50 ) can probably reveal this extra water loss/exchange channel.

Data availability
The study is reported in accordance with ARRIVE guidelines (https:// arriv eguid elines. org). All data described in the manuscript are in the database system of the Centre for Isotope Research, and are available upon request.